BS EN 13906-3-2014 Cylindrical helical springs made from round wire and bar Calculation and design Torsion springs《圆形线材和棒材制柱形螺旋弹簧 计算和设计 扭矩弹簧》.pdf

1、BSI Standards PublicationBS EN 13906-3:2014Cylindrical helical springs madefrom round wire and bar Calculation and designPart 3: T o r s i o n s p r i n g sBS EN 13906-3:2014 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN 13906-3:2014.It supersedes BS EN 13906-

2、3:2001 which is withdrawn.The UK participation in its preparation was entrusted to TechnicalCommittee FME/9/3, Springs.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contra

3、ct. Users are responsible for its correctapplication. The British Standards Institution 2014. Published by BSI StandardsLimited 2014ISBN 978 0 580 82233 9ICS 21.160Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority

4、of theStandards Policy and Strategy Committee on 28 February 2014.Amendments issued since publicationDate Text affectedBS EN 13906-3:2014EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN 13906-3 January 2014 ICS 21.160 Supersedes EN 13906-3:2001English Version Cylindrical helical springs made fro

5、m round wire and bar - Calculation and design - Part 3: Torsion springs Ressorts hlicodaux cylindriques fabriqus partir de fils ronds et de barres - Calcul et conception - Partie 3: Ressorts de torsion Zylindrische Schraubenfedern aus runden Drhten und Stben - Berechnung und Konstruktion - Teil 3: D

6、rehfedernThis European Standard was approved by CEN on 10 November 2013. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliogra

7、phical references concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibil

8、ity of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic

9、of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISAT

10、ION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2014 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN 13906-3:2014 EBS EN 13906-3:2014EN 13906-3:2014 (E) 2 Contents Page Foreword 3

11、 1 Scope 4 2 Normative references 4 3 Terms and definitions, symbols, units and abbreviated terms 4 3.1 Terms and definitions . 4 3.2 Symbols, units and abbreviated terms 5 4 Theoretical torsion spring diagram . 7 5 Design Principles . 10 5.1 General 10 5.2 Design of the ends . 10 5.3 Mounting of th

12、e ends 11 5.4 Design of the spring body 11 6 Types of loading 12 6.1 General 12 6.2 Static and quasi-static loading . 12 6.3 Dynamic loading 12 7 Stress correction factor q . 13 8 Material property values for the calculations of springs . 14 9 Design formulate 15 9.1 Design assumptions 15 9.2 Formul

13、ae . 15 9.2.1 General 15 9.2.2 Spring torque . 15 9.2.3 Angular spring rate 15 9.2.4 Developed length of active coils 16 9.2.5 Nominal diameter of wire or bar . 16 9.2.6 Inside coil diameter of the spring 16 9.2.7 Outside coil diameter of the spring . 16 9.2.8 Body length of the spring (excluding en

14、ds) . 16 9.2.9 Number of active coils 16 9.2.10 Torsional angle 16 9.2.11 Spring work 17 9.2.12 Uncorrected bending stress . 17 9.2.13 Corrected bending stress . 17 10 Permissible bending stress 20 10.1 Permissible bending stress under static or quasi-static loading . 20 10.2 Permissible stress rang

15、e under dynamic loading 20 10.2.1 Fatigue strength values 20 10.2.2 Permissible stress range 20 10.2.3 Lines of equal stress ratio 21 Bibliography 22 BS EN 13906-3:2014EN 13906-3:2014 (E) 3 Foreword This document (EN 13906-3:2014) has been prepared by Technical Committee CEN/TC 407 “Project Committe

16、e - Cylindrical helical springs made from round wire and bar - Calculation and design”, the secretariat of which is held by AFNOR. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by July 2014, and co

17、nflicting national standards shall be withdrawn at the latest by July 2014. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN and/or CENELEC shall not be held responsible for identifying any or all such patent rights. This docum

18、ent supersedes EN 13906-3:2001. This European Standard has been prepared by the initiative of the Association of the European Spring Federation ESF. This European Standard constitutes a revision of EN 13906-3:2001 for which it has been technically reviewed. The main modifications are listed below: u

19、pdating of the normative references; technical corrections. EN 13906 consists of the following parts, under the general title Cylindrical helical springs made from round wire and bar Calculation and design: Part 1: Compression springs; Part 2: Extension springs; Part 3: Torsion springs. According to

20、 the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece

21、, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. BS EN 13906-3:2014EN 13906-3:2014 (E) 4 1 Scope This European Standard specifies the calculation an

22、d design of cold and hot coiled cylindrical helical torsion springs with a linear characteristic, made from round wire and bar of constant diameter with values according to Table 1. Table 1 Characteristic Cold coiled torsion spring Hot coiled torsion springaWire or bar diameter d 20 mm d 10 mm Numbe

23、r of active coils n 2 n 2 Spring index 4 w 20 4 w 12 aThe user of this European Standard shall pay attention to the design of hot coiled springs, because there can be differences between the design and a real test. 2 Normative references The following documents, in whole or in part, are normatively

24、referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 10089, Hot-rolled steels for quenched and tempered springs - Techn

25、ical delivery conditions EN 10270-1, Steel wire for mechanical springs - Part 1: Patented cold drawn unalloyed spring steel wire EN 10270-2, Steel wire for mechanical springs - Part 2: Oil hardened and tempered spring steel wire EN 10270-3, Steel wire for mechanical springs - Part 3: Stainless sprin

26、g steel wire EN 12166, Copper and copper alloys - Wire for general purposes EN ISO 26909:2010, Springs - Vocabulary (ISO 26909:2009) ISO 26910-1, Springs - Shot peening - Part 1: General procedures 3 Terms and definitions, symbols, units and abbreviated terms 3.1 Terms and definitions For the purpos

27、es of this document, the terms and definitions given in EN ISO 26909:2010 and the following apply. 3.1.1 spring mechanical device designed to store energy when deflected and to return the equivalent amount of energy when released SOURCE: EN ISO 26909:2010, 1.1 3.1.2 torsion spring spring that offers

28、 resistance to a twisting moment around the longitudinal axis of the spring SOURCE: EN ISO 26909:2010, 1.4 BS EN 13906-3:2014EN 13906-3:2014 (E) 5 3.1.3 helical torsion spring torsion spring normally made of wire of circular cross-section wound around an axis and with ends suitable for transmitting

29、a twisting moment SOURCE: EN ISO 26909:2010, 3.14 3.2 Symbols, units and abbreviated terms Table 2 contains the symbols, units and abbreviated terms used in this standard. Table 2 Symbols Units Terms DA mm coil diameter tolerance of the unloaded spring a mm gap between active coils of the unloaded s

30、pring ei2DDD+= mm mean diameter of coil dD mm mandrel diameter eD mm outside diameter of the spring eDmm outside coil diameter of the spring when deflected through and angle in the direction of the coiling hD mm housing diameter iD mm inside diameter of the spring iD mm inside coil diameter of the s

31、pring when deflected through and angle in the direction of the coiling pD mm test mandrel diameter d mm nominal diameter of wire (or bar) maxd mm upper deviation of d Rd mm diameter of loading pins E N/mm2(MPa) modulus of elasticity (or Youngs modulus) F N spring force . ,21FF N spring forces for th

32、e torsional angles . ,21 and related lever arms BA, RR at ambient temperature of 20 C nF N spring force for the maximum permissible angle n and the lever arms BA, RR KL mm body length of the unloaded spring for close-coiled springs (excluding ends) K0L mm body length of the unloaded spring for open-

33、coiled springs (excluding ends) KLmm body length of close-coiled spring deflected through an angle (excluding ends) l mm developed length of active coils (excluding ends) ,BAllmm length of ends M N mm spring torque BS EN 13906-3:2014EN 13906-3:2014 (E) 6 Symbols Units Terms . ,21MMN mm spring torque

34、 for the angles . ,21 and related lever arms BA, RR at ambient temperature of 20 C nMN mm spring torque for the maximum permissible angle, nmaxMN mm maximum spring torque, which occurs occasionally in practice, in test or during assembly of the spring N - number of cycles up to rupture n - number of

35、 active coils q - stress correction factor (depending on D/d) , ,BARRR mm effective lever arms of spring mRN/mm2(MPa) minimum value of the tensile strength MRRNmm/Deg angular spring rate (increase of spring torque per unit angular deflection) nBA. , , rrrr mm inner bending radii Wmm3sectional moment

36、 W N mm spring work =Dwd- spring index z - decimal values of the number of active coils n Deg torsional angle . ,21Deg torsional angle corresponding to spring torque M1, M2. to the spring forces F1, F2. nDeg maximum permissible torsional angle Deg corrected torsional angle in the case of a long, unc

37、lamped radial end Deg corrected torsional angle in the case of a long, unclamped tangential end hDeg angular deflection of spring (stroke) between two positions and 21 maxDeg maximum torsional angle which occurs occasionally in practice, in test or by mounting of the spring Deg increase of torsional

38、 angle due to deflection of a long, unclamped radial end Deg increase of torsional angle due to deflection of a long, unclamped tangential end Deg angle of tangential legs of unloaded spring 0Deg angle of active coils of unloaded spring 0Deg relative end fixing angle for unloaded spring n. , 21Deg r

39、elative end fixing angle, corresponding to torsional angles n21. , kg/dm3density N/mm2(MPa) uncorrected bending stress (without the influence of the wire curvature being taken into account) . ,21N/mm2(MPa) uncorrected bending stress for the spring torques M1, M2BS EN 13906-3:2014EN 13906-3:2014 (E)

40、7 Symbols Units Terms n N/mm2(MPa) uncorrected bending stress for the spring torque MnqN/mm2(MPa) corrected bending stress (according to the correction factor q) . ,2q1q N/mm2(MPa) corrected bending stress for the spring torques . ,21MM qhN/mm2(MPa) corrected bending stress for the stroke h qHN/mm2(

41、MPa) corrected bending stress range in fatigue strength diagram qON/mm2(MPa) corrected maximum bending stress in the fatigue strength diagram qUN/mm2(MPa) corrected minimum bending stress in the fatigue strength diagram zulN/mm2(MPa) permissible bending stress A BC, , Deg bending angle of the end 4

42、Theoretical torsion spring diagram The illustration of the torsion spring corresponds to EN ISO 2162-1:1996, Figure 6.1. The theoretical torsion spring diagrams are given in Figure 1. BS EN 13906-3:2014EN 13906-3:2014 (E) 8 Figure 1 Theoretical torsion spring diagram Figure 2 to Figure 4 show differ

43、ent types of torsion springs and/or their end. The recommended arrangements are given in 5.3. BS EN 13906-3:2014EN 13906-3:2014 (E) 9 Figure 2 Open coiled torsion spring Figure 3 Torsion spring with tangential ends BS EN 13906-3:2014EN 13906-3:2014 (E) 10 AB360 =Z (1) ( )iAAarcsin22+=+rdD dr(2) ( )i

44、Barcsin22BB+=+rdD dr(3) Figure 4 Torsion spring with radial ends 5 Design Principles 5.1 General For the design of torsion springs, besides the housing space, the required maximum spring torque Mmax,the related torsional angle maxand the permissible dynamic stresses (see 10.1 and 10.2) are decisive.

45、 If the torsion spring is guided on a mandrel or in a housing, care shall be taken to ensure enough clearance remains between the spring and its guide. Reference values for the mandrel diameter are: ( )d iDmax0,95 x360+nD= D A dan(4) and for the housing diameter: ( )ehDmax1, 0 5 x360+nD= D A dan(5)

46、Furthermore, 5.2 and 5.4 and Clause 6 shall be taken into account. 5.2 Design of the ends The ends can be adapted in many different ways to the requirements of a particular application. In the interest of economic manufacture the simplest possible design of the spring ends should be aimed at, i.e. t

47、angential ends. For the sake of obtaining in the design a reproducible spring characteristic and an adequate standard of accuracy it is always desirable that both ends should be clamped. Clamping is any type of fixing which introduces a couple (see also 9.1). The minimum internal bending radius r at

48、 the ends shall not be smaller than the wire diameter d. The lengths lA, lB.lnof straight ends or straight parts of ends, between two bends shall be at least 3d. BS EN 13906-3:2014EN 13906-3:2014 (E) 11 5.3 Mounting of the ends Figure 5 and Figure 6 show the recommended arrangements. Preferably load

49、ed legs should be clamped. a) b) c) Figure 5 Clamped end Figure 6 Not clamped end 5.4 Design of the spring body In order to avoid frictional forces the coils should not bear against one another or should exert only a small amount of pressure on one another. If a longer mounting space shall be filled by increasing a, the maximum permissible gap between active coils of the unloaded spring will be: ( )max0,830,24 0